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Theorem unieqi 3618
Description: Inference of equality of two class unions. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
unieqi.1  |-  A  =  B
Assertion
Ref Expression
unieqi  |-  U. A  =  U. B

Proof of Theorem unieqi
StepHypRef Expression
1 unieqi.1 . 2  |-  A  =  B
2 unieq 3617 . 2  |-  ( A  =  B  ->  U. A  =  U. B )
31, 2ax-mp 7 1  |-  U. A  =  U. B
Colors of variables: wff set class
Syntax hints:    = wceq 1259   U.cuni 3608
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-uni 3609
This theorem is referenced by:  elunirab  3621  unisn  3624  uniop  4020  unisuc  4178  unisucg  4179  univ  4235  dfiun3g  4617  op1sta  4830  op2nda  4833  dfdm2  4880  iotajust  4894  dfiota2  4896  cbviota  4900  sb8iota  4902  dffv4g  5203  funfvdm2f  5266  riotauni  5502  1st0  5799  2nd0  5800  unielxp  5828  brtpos0  5898  recsfval  5962  uniqs  6195  xpassen  6335  sup00  6407
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